Math Problem Statement
5(3-2i)+2i(4+6i)=
Solution
To simplify the expression , we’ll expand each term and then combine like terms.
Step 1: Expand
Step 2: Expand
Since , replace with :
Step 3: Combine Terms
Now, add the results from Step 1 and Step 2:
Combine like terms (real parts and imaginary parts):
- Real part:
- Imaginary part:
Final Answer
Would you like a deeper explanation or have any further questions?
Here are five related questions to consider:
- How would the answer change if were replaced with a different imaginary unit?
- What is the geometric interpretation of the complex number on the complex plane?
- How can we factor expressions involving complex numbers?
- How do we multiply complex numbers using polar form?
- What other mathematical properties are unique to complex numbers?
Tip: Always remember that ; this substitution is essential in simplifying expressions with complex numbers.
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Algebraic Expansion
Imaginary Unit
Formulas
Distributive Property a(b + c) = ab + ac
i^2 = -1
Theorems
Properties of Complex Numbers
Arithmetic of Complex Numbers
Suitable Grade Level
Grades 10-12
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